Sampling distribution

Suppose that X1, X2,....Xm and Y1,Y2,....,Yn are independent random samples, with the variables Xi normally distributed with mean and variance and the variables Yi normally distributed with mean and variance . The difference between the sample means, is then a linear combination of m + n normally distributed random variables and is itself normally distributed.

Suppose that = 2, = 2.5, and m=n. Find the sample sizes so that ( ) will be within 1 unit of ( ) with probability .95.

Suppose that X1, X2,....Xm and Y1,Y2,....,Yn are independent random samples, with the variables Xi normally distributed with mean and variance and the variables Yi normally distributed with mean and variance . The difference between the sample means, is then a linear combination of m + n normally distributed random variables and is itself normally distributed.

Suppose that = 2, = 2.5, and m=n. Find the sample sizes so that ( ) will be within 1 unit of ( ) with probability .95.